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Covering Multiple Objectives with a Small Set of Solutions Using Bayesian Optimization
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Proposes MOCOBO, a trust-region Bayesian optimization method that finds a small covering set of K<T solutions by maximizing a coverage score, using a new expected coverage improvement (ECI) acquisition function with greedy submodular approximation.
Problem
Black-box multi-objective optimization where, instead of a single Pareto set, one needs K<T solutions that collectively cover (have at least one good solution for) all T objectives, e.g., finding a few antibiotics that together treat T pathogens.
Approach
Defines a coverage score (sum over objectives of the max over solutions) and a coverage analog of expected improvement (ECI); the best observed covering set is approximated greedily via submodular optimization, and K trust regions centered on the covering set run in parallel (TuRBO-M style) with q-ECI batch acquisition.
Key results
- MOCOBO's K-solution covering sets nearly match the coverage of T individually optimized solutions across tasks, and consistently outperform baselines including CluSO, TuRBO, ROBOT, and MORBO.
- In vitro, MOCOBO-found peptides covered 9 of 11 drug-resistant or hard-to-kill pathogens with high potency, with moderate activity on 1 of 11.
- Ablations show trust regions and the ECI acquisition function each significantly improve performance over removing them (MOCOBO-EIT still outperforms other baselines).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MOCOBO to find K=2 solutions instead of using T individually optimized solutions (ablation) | Rover, T=3 pairwise-conflicting courses · Rover, T=3 pairwise-conflicting courses, K=2 | average coverage score: 2.932 vs 12.899 | Hurt |
| Use K=1 rather than K=2, 3, or 4 solutions (ablation) | MOCOBO · Rover, T=4 obstacle courses | final coverage score | Hurt |
| Increase K from 2 to 3 or 4 (ablation) | MOCOBO · Rover, T=4 obstacle courses | optimization convergence | Helped |
| Use K=2 instead of a higher covering-set size (ablation) | MOCOBO · Rover, T=4 obstacle courses | optimization efficiency | Hurt |
| Increase surrogate inducing points from m=1024 to m=4096 (ablation) | MOCOBO · Rover, T=4 obstacle courses | coverage performance | No clear effect |
| Reduce surrogate inducing points to m≤256 (ablation) | MOCOBO · Rover, T=4 obstacle courses | coverage performance | Hurt |
| Vary acquisition batch size q among 1, 2, 5, 10, 20, and 40 (ablation) | MOCOBO · Rover, T=4 obstacle courses | coverage performance | No clear effect |
| Remove trust regions (ablation) | MOCOBO · Rover, T=4 obstacle courses | coverage performance | Hurt |
| Replace ECI with the maximum of standard EI across individual objectives (EIT) (ablation) | MOCOBO · Rover, T=4 obstacle courses | coverage performance | Hurt |
| Use an oracle objective partition and optimize one solution per subset (ablation) | MOCOBO · Three optimization tasks in the oracle-partition ablation | best coverage score | No clear effect |
| Use MOCOBO for coverage optimization rather than CluSO | High-dimensional and structured tasks · Optimization tasks evaluated in the paper | coverage score | Helped |
| Use MOCOBO to find K solutions rather than a baseline method | High-dimensional coverage optimization tasks · Optimization tasks evaluated in the paper | coverage score | Helped |
Surprising findings
- A variant using per-objective EI maximum (MOCOBO-EIT) still outperformed all other baselines, indicating much of the gain comes from other components.
- CluSO performed substantially worse than even baselines not designed for coverage.
Limitations
- Assumes some objectives are conflicting so that K<T can cover all; if all pairs conflict, K<T coverage is poor (ablation shows much lower coverage than T individual optima).
- Requires domain knowledge to choose K large enough to approach the T-solution ceiling.
- Greedy approximation gives only (1-1/e) guarantee; GP surrogate is approximate (PPGPR).
Experimental setup
Datasets: 4.5 million amino acid sequences (VAE pre-training) Guacamol Ranolazine MPO task pyiqa image quality metrics Stanford Memorial Church and desk HDR images
Benchmarks: peptide design (template free and template constrained, APEX 1.1 MIC) Ranolazine MPO multi-element molecule design rover trajectory optimization (T=4,8,12) image tone mapping (pyiqa metrics)
Metrics: coverage score MIC in vitro MIC
Baselines: CluSO TuRBO ROBOT MORBO LOL-BO random sampling
Builds on: TuRBO expected improvement PPGPR SCBO LOL-BO
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